Question

The difference of two numbers is 3, and the sum of three times the larger one and twice the smaller one is 19. Find the two numbers.

Answer 1

Let the larger number be x and the smaller number be y.
According to given information, we have
x - y = 3
⇒ x - 3 + y   ....(i)
Also, 3x + 2y = 19
⇒ 3(3 + y) + 2y = 19    ....[From (i)]
⇒ 9 + 3y + 2y = 19
⇒ 5y = 10
⇒ y = 2
⇒ x = 3 + 2
= 5
Thus, the required numbers are 5 and 2 respectively.